In an electric drive system for a vehicle known in the related art, a cooling medium circulation path is formed in an electric drive device that electrically drives the vehicle, a target flow rate for a cooling medium flowing through refrigerant piping is determined based upon an electric motor current command value and a refrigerant circulation pump is driven based upon the target flow rate (see, for instance, patent literature 1). Such a cooling system is considered to assure a high level of responsiveness with which the refrigerant is supplied in a quantity corresponding to the extent of temperature increase occurring as heat is generated at the electric drive device where the electric motor current, i.e., the required drive force, is expected to rise.